NTA JEE Main 3rd September 2020 Shift 1

Consider the two sets:
$$A = \{m \in R : \text{both the roots of } x^2 - (m+1)x + m + 4 = 0 \text{ are real}\}$$ and $$B = [-3, 5)$$
Which of the following is not true?

If $$\alpha$$ and $$\beta$$ are the roots of the equation $$x^2 + px + 2 = 0$$ and $$\frac{1}{\alpha}$$ and $$\frac{1}{\beta}$$ are the roots of the equation $$2x^2 + 2qx + 1 = 0$$, then $$\left(\alpha - \frac{1}{\alpha}\right)\left(\beta - \frac{1}{\beta}\right)\left(\alpha + \frac{1}{\beta}\right)\left(\beta + \frac{1}{\alpha}\right)$$ is equal to:

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is:

The value of $$(2 \cdot {}^1P_0 - 3 \cdot {}^2P_1 + 4 \cdot {}^3P_2 - \ldots$$ up to 51$$^{th}$$ term$$) + (1! - 2! + 3! - \ldots$$ up to 51$$^{th}$$ term) is equal to

If the number of integral terms in the expansion of $$\left(3^{\frac{1}{2}} + 5^{\frac{1}{8}}\right)^n$$ is exactly 33, then the least value of $$n$$ is

Let P be a point on the parabola, $$y^2 = 12x$$ and N be the foot of the perpendicular drawn from P, on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the $$y$$-intercept of the line NQ is $$\frac{4}{3}$$, then:

A hyperbola having the transverse axis of length $$\sqrt{2}$$ has the same foci as that of the ellipse, $$3x^2 + 4y^2 = 12$$ then this hyperbola does not pass through which of the following points?

Let $$[t]$$ denote the greatest integer $$\leq t$$. If $$\lambda \in R - \{0, 1\}$$, $$\lim_{x \to 0}\left|\frac{1 - x + |x|}{\lambda - x + [x]}\right| = L$$, then $$L$$ is equal to

The proposition $$p \to \sim(p \wedge \sim q)$$ is equivalent to:

For the frequency distribution: Variate $$(x)$$: $$x_1, x_2, x_3, \ldots, x_{15}$$
Frequency $$(f)$$: $$f_1, f_2, f_3, \ldots, f_{15}$$
where $$0 < x_1 < x_2 < x_3 < \ldots < x_{15} = 10$$ and $$\sum_{i=1}^{15} f_i > 0$$, the standard deviation cannot be